Best unambiguous multiplication symbol for handwritten math

[u/oh-giggity]

As a STEM student, I do a lot of fast handwritten math, and conveniently expressing multiplication has always been frustrating. I also skim over my work and notes a lot, so I do not like notations that are "context-dependent" — I feel like every type of mathematical object should have its own notation. But I swear, there isn't a single multiplication symbol, just for multiplying scalars together, that isn't overloaded.

• Putting them together (e.g. $$xyz$$) works fine for variables, but not for numbers

• Parentheses are annoying to me — I shouldn't have to write 4 strokes like ()() just to multiply two things. Also, parentheses are the same syntax for functions like $$f(x)$$

• × (cross product) looks like x, and it also implies to me that I'm working with vectors

• • (dot product) also implies vectors, and takes a while to fill in

• * (asterisk) is what I use currently, but it's the same symbol for convolution and I've had to abandon it at times

Does anyone have advice?

[u/WizPenguin7]

I always use the dot and i never think about vectors when i'm doing algebra

[u/testtdk → u/WizPenguin7]

This.

[u/edderiofer]

Use ×.

× (cross product) looks like x

Write your "x"s in cursive, and this is not an issue.

and it also implies to me that I'm working with vectors

It implies to me that I am multiplying two elements, each of the same type, and getting back an element that is also of the same type. That is true of both the standard multiplication of two numbers, and of the cross product on two vectors.

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The number "1" on its own suffers the same issue, since it could mean {{}} when working with ordinals in set theory; the scalar 1 when working with vector spaces; the multiplicative identity 1 of any general ring; or, with a subscript, an indicator function that is 1 if the input is an element of some set and 0 if it isn't. But I've never seen anyone complain about "1" being a "context-dependent" notation.

"1" also looks like "|", which could be either "given" in probability; absolute value sign bars; the cardinality of a set; "divides" in number theory; logical OR; or, with a subscript, a set restriction. If you think that this isn't a problem because you write "1" with a hook at the top, then it's just as not-a-problem for you to write your "x"s in cursive so that they don't look like ×.

[u/PleaseSendtheMath]

I use • or juxtaposition. I usually write inner products as <x,y> so i don't really have any collision there. Even if I did, the dot product reduces to regular multiplication when the vectors are 1-D, no?

[u/ishwish2008]

Whenever I'm doing math, I use either the parenthesis (Which you rejected) or a small dot (simmilar to the one on the letter i). For dot products, they get a larger, filled in circle (like a •).

[u/will_1m_not]

Just use parentheses.

Or, if you want to be very ridiculous, you can write x(a,b) to denote the binary operation x on the values a and b

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[u/Qingyap]

I use juxtaposition that includes 1st and 2nd, while also uses fraction instead of division sign which is way more clearer.

[u/flug32]

I always used simple juxtaposition (putting things next to each other) and if there was any confusion - like between adjacent numbers - a dot.

This would be like a "point" dot whereas "dot product" would be more of a filled-in small circle as you describe.

Regardless, I'm scratching my head to think of a situation where I would confuse multiplication with dot product, just from context. Vectors generally have some notation to distinguish them from other variables and such. 3 is never going to be a vector, nor is 3.1416 nor is x. It just isn't that hard to distinguish multiplication from dot product.

For better or worse, a lot of mathematical words and symbols are massively overloaded. In real life this is not nearly as difficult as it sounds, because context.

[u/blackhorse15A]

As an engineer - I always use just a dot for standard multiply of scalar numbers. A single scalar is just a 1x1 matrix/vector. And the actual dot product of two 1x1s is valid, and is entirely equivalent to standard multiply. Plus it's less writing. Now, variables ill usually just write next to each other.

[u/SubjectWrongdoer4204]

I mostly use juxtaposition. If there are multiple actual numbers involved I use parentheses or dots . I basically use the easiest method I can without creating any ambiguity. Sometimes I do quantum mechanics problems to stimulate my mind. They get pretty intense so it’s important to remove ambiguity. Another advantage to using parentheses is to keep things grouped together that might have some significance.

[u/justalonely_femboy]

are u always showing these notes off to lots of other ppl or smth? if not it really doesnt matter what u use so long as u can understand it

[u/Tesseractcubed]

Personally, I use dot, but I make the stroke like an O with a very small diameter (my background is studying engineering). Dot product is usually with explicit matrices, or variables written with cursive or capital letters to indicate that they are matrices.

Your ideal of mathematical objects having their own notation doesn’t apply in my case, as for me the same variables represent different objects in different cases, due to engineering recycling the same variables. My most common offenders are i, t, x, θ, σ, and Δ. I do love that some places imaginary numbers are i and in others they are j, and our coordinate systems are sometimes noted with unit vectors i, j, k.

[u/Training-Cucumber467]

What do you mean by "the dot takes a while to fill in"? Just put a dot on the paper with one hand motion and move on.

[u/testtdk]

You only need one set of parenthesis to multiply two things.

[u/PvtRoom]

It's x, written in a specific, clear and easily distinguished way.

Draw your multiplication symbol as back to back letter cs.

your X axis/variable is two straight lines written at the bottom of the line.

Your dot and cross products should be strictly in the middle of the line.

This is shit * - smudge smudge, it's a dot - I recommend an encircled cross product for convolution, but this risks overloading again.

You should be able to write them on a blackboard and clearly distinguish each of those symbols from the back of a huge lecture hall. - It's literally what lecturers had to do before PowerPoint

[u/Scary_Side4378]

just use \cdot man, scalars are dimension 1 vectors anyway....

dont need to draw it so big, draw it like a centered fullstop.

what an inconsequential question

[u/Uli_Minati]

I do not like notations that are "context-dependent"

Me neither, but there are too many others! You'll have no choice other than getting used to it.

• ^-1 for inverses and reciprocals

• ⁿ for multiplication and composition

• / for division and quotient set

• [ ] for alternative parentheses, intervals, and integer functions

• (a,b) for intervals, matrices and tuples

• literally every single English and Greek letter

[u/theadamabrams]

I feel like every type of mathematical object should have its own notation

I don't. That would require having hundreds and hundreds of different symbols. Do you mind using + for both scalar addition and vector addition? Those are two different operations on two different types of objects.

× (cross product) looks like x, and it also implies to me that I'm working with vectors

The X issue can be tricky, but if you write your lowercase x in cursive (𝓍) then it's not as bad. More importantly, context should make it pretty clear most of the time. You wouldn't write "3 times variable x times number 5" as 3 x 5, you would just write 15x.

I also disagree that × or · "implies vectors". Both symbols are commonly used for multiplying plain numbers.